the sum of two numbers is 43. the larger number is 9 more than the smaller number. what are the numbers
x + 9 + x = 43
2x = 34
x = 17
21
To find the two numbers, let's represent them as variables. Let's call the smaller number "x" and the larger number "y".
From the given information, we have two equations:
1) The sum of the two numbers is 43: x + y = 43
2) The larger number is 9 more than the smaller number: y = x + 9
We can solve this system of equations using substitution or elimination method.
Using the substitution method:
Step 1: Solve equation 2 for y in terms of x.
y = x + 9
Step 2: Substitute y in equation 1 with the value of y from equation 2.
x + (x + 9) = 43
2x + 9 = 43
Step 3: Simplify the equation.
2x = 43 - 9
2x = 34
Step 4: Solve for x by dividing both sides by 2.
x = 34 / 2
x = 17
Step 5: Substitute the value of x back into equation 2 to find y.
y = 17 + 9
y = 26
Therefore, the smaller number is 17 and the larger number is 26.